I am currently building out my attic in my 1912 home. I want to use R19 insulation with baffling on the cathedral ceiling. I want to then install 1x6 tongue & groove paneling. My rafters are 2x6's and are 24" apart. The unsupported span from eave to peak is roughly 13 1/2'. The pitch of my roof is 8/12.

I have been told that I should "sister" my rafters because the load of the insulation and paneling will eventually make the roof sag and I need more load-bearing support.

I would like to know if this is sound advice and if there is a better alternative, or if anything more is even necessary.

It's hard to compare 2x6 of today with wood that was cut 100 years ago. If the house was built today it would be built with 2x10s so you would have room for 8" of insulation and air flow above that. I wood sister just for the insulation value.

nealtw is correct. A full 2" x 6" rafter will support more than today's 1.5" x 5.375" lumber called a 2 x 6. I looked at a span calculator at http://planhelp.com/public/98.cfm. It calls for a 2x8 douglas fir or a 2x10 southern pine to support just the roof load. Your best bet if you want to be sure is to consult a structural engineer before you add to much load to the roof and then find out it sagged. They will have the ability to determine what species and dimensions your rafters are now and other considerations not available to anyone here. Probably be worth your money so you don't spend to much on material and still are not sure you have fixed any problems. I guess you could estimate the extra load you will add and try to plug that load into the span calculator. Let us know how it goes.

Knowing your own body weight, stand on the roof directly above a rafter midpoint and have a helper measure the deflection due to the concentrated load you are imposing. Finding what distributed load your rafter can presently support is tedious but possible.
What is your roofing material? Is the 13.5' measured along the rafter or measured horizontally?

Even if the span load is ok I would add 3 1/2" just for insulation. 2x10s may be cheaper than an engineer.

I also use the Pro-Desk at my local Home Depot for things like this. I do quite a bit of buisness with them and I have had them call their design people to answer questions about structural loading. Probably helps that they can then sell me the material to do the job. But it costs nothing and gives me a place to start without over designing.